答案 1

Question

这个问题导致了一个新的方案的出现：

pst-venn

您看到我的代码并请回答我的两个问题：

\documentclass{article}
\usepackage{amsmath,amssymb,mathptmx}
\usepackage{pstricks}
\usepackage{pst-node}
\usepackage{auto-pst-pdf}
\begin{document}
\begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
  \psclip{% 
        \pscircle(0,0){3}
        \pscircle(4,0){3} }
        \pscircle[fillcolor=blue,fillstyle=solid](2,3){3}        
  \endpsclip
 \pscircle(0,0){3}
 \pscircle(4,0){3}
 \pscircle(2,3){3}
\end{pspicture}    
\end{document}

输出图片：

图片1：

其代码（使用 Ti钾韓國語：

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3); 
\end{tikzpicture}

我的问题：

• 如何让我的图片像图片 1 那样？我真的不知道如何给它填充颜色。

• （完成上一个问题后）你看到 Ti钾图片 1 的 Z 代码？看看重要的选项even odd rule。PStricks 是否有与 Ti 相同的命令、宏……钾Z？

注意：我更喜欢 PStricks 而不是 Ti钾Z，但有时我能认出 Ti钾Z 代码更好。

如果让您感到不舒服，我很抱歉。

Answer 1

PSTricks 解决方案只是为了好玩！

答案 1

\documentclass[pstricks]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\pscustom[fillstyle=eofill,fillcolor=blue]
{ 
  \pscircle(1.5;90){3}
  \pscircle(1.5;-30){3} 
  \pscircle(1.5;210){3} 
} 
\end{pspicture} 
\end{document}

仅由于一个微不足道的原因，笔触颜色保留为黑色。

使用笛卡尔坐标来响应请求。

\documentclass[pstricks]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\pscustom[fillstyle=eofill,fillcolor=blue]
{ 
  \pscircle(0,1.5){3}
  \pscircle(1.29,-0.75){3} 
  \pscircle(-1.29,-0.75){3} 
} 
\end{pspicture} 
\end{document}

答案 2

非零缠绕规则：

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=solid,fillcolor=red]
{
    \pscircle{1}
    \pscircle{2}
}
\end{pspicture} 
\end{document}

非零缠绕规则：

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=solid,fillcolor=red]
{
    \psarcn(0,0){1}{360}{0}
    \pscircle{2}
}
\end{pspicture} 
\end{document}

奇偶规则：

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=eofill,fillcolor=red]
{
    \pscircle{1}
    \pscircle{2}
}
\end{pspicture} 
\end{document}

Answer 2

以下是基于 @Thomas 的答案。差异

• “基本”区域 I、II、...、VIII 的编号并不相同。我的编号是“N”是罗马数字“n+1”，其中二进制中的“n”是“abc”，并且该区域是 A 或非 A 与 B 或非 B 与 C 或非 C 的交集，根据 a、b、c = 0 或 1。（布尔逻辑）

• 该宏只需要一个输入：集合的 TeX 公式。请通过添加适当的定义来丰富语法，将 TeX 数学宏转换为布尔逻辑符号，以便xintexpr

• 我已经放弃了所有花哨的颜色定制，但如果需要，xparse virtuosos 会添加花哨的可选参数来重新安装它。

因此，这里的重点是xintexpr根据 TeX 排版公式自动计算图表中需要填充的区域。

注意\setminus它必须可以带括号使用\setminus (...)，也可以不带括号使用，但只能带一个字母\setminus A ok，\setminus A\cap B不 ok，因为这里对 xintexpr boolean 的翻译将天真地执行与 等同的操作and not(A) and B，而不是预期的and not(A and B)。简而言之，您必须将\setminus其视为具有最大约束优先级。

\documentclass[pstricks, border=10pt]{standalone}
\usepackage{pst-node}
\usepackage{xparse,xintexpr}

\def\KOEA{1.9,2.2}
\def\FOEA{1.4,1}

\def\KOEB{3.3,2.2}
\def\FOEB{1.2,1}

\def\KOEC{2.75,1.4}
\def\FOEC{1.4,1}

\def\KOEO{2.5,2}
\def\FOEO{2.5,2.0}

\NewDocumentCommand{\EreignisA}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEA)(\FOEA)}{%
\psellipse(\KOEA)(\FOEA)}%
}

\NewDocumentCommand{\EreignisB}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEB)(\FOEB)}{%
\psellipse(\KOEB)(\FOEB)}%
}

\NewDocumentCommand{\EreignisC}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEC)(\FOEC)}{%
\psellipse(\KOEC)(\FOEC)}%
}

\NewDocumentCommand{\EreignisOmega}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEO)(\FOEO)}{%
\psellipse(\KOEO)(\FOEO)}%
}

\NewDocumentCommand{\EndeEllipsen}{sm}{%
\EreignisOmega%
\pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
\pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
\EreignisA
\EreignisB
\EreignisC
\rput[t](E){#2}%
\IfBooleanF{#1}{%
\rput(Omega){$\Omega$}\pcline[nodesepA=0.25](Omega)(MOmega)
\rput(A){$A$}\pcline[nodesepA=0.25](A)(MA)
\rput(B){$B$}\pcline[nodesepA=0.25](B)(MB)
\rput(C){$C$}\pcline[nodesepA=0.2](C)(MC)
}%
}

\NewDocumentCommand{\codeclip}{m}{%
\pscustom[linestyle=none]{%
 \code{/clip /eoclip load def}%
  \psframe(-\maxdimen,-\maxdimen)(\maxdimen,\maxdimen)
  #1
  }%
}

%\ExplSyntaxOn
% We could use some automated macro creation but well
% 000
\NewDocumentCommand{\arealI}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisOmega*[#1][#2]%
\endpsclip
}%
% 001
\NewDocumentCommand{\arealII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}
% 010
\NewDocumentCommand{\arealIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisB*[#1][#2]%
\endpsclip
}
% 011
\NewDocumentCommand{\arealIV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisA
}%
}%
\EreignisB*[#1][#2]%
\EreignisC*[#1][#2]%
\endpsclip
}
% 100
\NewDocumentCommand{\arealV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}
% 101
\NewDocumentCommand{\arealVI}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisC
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisA*[#1][#2]%
\EreignisC*[#1][#2]%
\endpsclip
}
% 110
\NewDocumentCommand{\arealVII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\EreignisB*[#1][#2]%
\endpsclip
}
% 111
\NewDocumentCommand{\arealVIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
}%
\codeclip{%
  \EreignisA
  \EreignisC
}%
\codeclip{%
  \EreignisB
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\EreignisB*[#1][#2]%
\EreignisC*[#1][#2]%
\endpsclip
}
%\ExplSyntaxOff

%\xintverbosetrue
\makeatletter
\newcommand\VennFromTeX[1]{%
    \VennFromTeX@main #1%
}%
\def\VennFromTeX@main$#1${%
    \begingroup
        \xintglobaldefstrue
        \def\overline##1{!(##1)}% or not(##1)
        \def\cap{&&}% or 'and'
        \def\cup{||}% or 'or'
        \def\oplus{ 'xor' }%
        \def\setminus##1{\ifx(##1&&!(\else &&!(##1)\fi}%
        \let\bigl\empty
        \let\bigr\empty
        % ....
        % (add above all needed extra definitions: \let\Bigl\empty etc...) 
    \xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
    \endgroup
    % we could make a loop here (using \@Roman), but let's stay simple
    % I trust xparse experts can wrap this up in macros allowing to customize
    % the colors
% ATTENTION THAT THESE \arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
    \xintifboolexpr{MyBool(0, 0, 0)}{\arealI[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(0, 0, 1)}{\arealII[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(0, 1, 0)}{\arealIII[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(0, 1, 1)}{\arealIV[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(1, 0, 0)}{\arealV[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(1, 0, 1)}{\arealVI[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(1, 1, 0)}{\arealVII[cyan][0.8]}{}%
    \xintifboolexpr{MyBool(1, 1, 1)}{\arealVIII[cyan][0.8]}{}%
    \EndeEllipsen{$#1$}%
}%
\makeatother

\begin{document}

%testing if I, II, ..., VIII are as expected
% \makeatletter
% \xintFor*#1in{\xintSeq{0}{7}}\do{%
% \begin{pspicture}(0,-1)(5,4)
% \rput(2,0){\the\numexpr1+#1}
% \@nameuse{areal\@Roman{\numexpr1+#1}}[cyan][0.8]
% \EndeEllipsen{}
% \end{pspicture}
% }%
% \end{document}


\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$A\cap B\cap C$}%
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$A\cap (B\cup C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$(\overline{A}\cap \overline{B})\cup C$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$\overline{A}\setminus (B\cap C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$(\overline{A}\setminus B)\cap C$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$(A\setminus B)\cup (B\cap C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$\bigl((A\cap B)\cup (A\cap C)\bigr)\setminus(A\cap B\cap C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennFromTeX{$A\oplus B\oplus C$}
\end{pspicture}

\end{document}

生产

---

---

这是生成全部 256 个维恩图的代码。只需将其插入上述文档的正文中，别忘了添加\usepackage{xintbinhex}到序言中。

% generating all graphics

% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (\overline{A}\cap \overline{B} \cap \overline{C})
% We want also to describe the region as a formula...
% We could use 8 \xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but \ifodd would be enough
% As I use xintbinhex, I also use a single \xintFor* loop

%\def\gobbleone#1{}%
\def\gobbletwo#1#2{}%
\xintFor* #1 in {\xintSeq{0}{255}}:
{%
   \xintDigitsOf\xintDecToBin{\the\numexpr256+#1\relax}\to\Regions
   % due to leading 1 there will be a shift of indexing in \Regions
   \edef\x{\xintifboolexpr{\Regions{\the\numexpr9-0}}% 000
              {\unexpanded{\allowbreak\cup
                           \overline{A}\cap\overline{B}\cap\overline{C}}}%
              {}%
           \xintifboolexpr{\Regions{9-1}}%  001
              {\unexpanded{\allowbreak\cup \overline{A}\cap\overline{B}\cap C}}%
              {}%
           \xintifboolexpr{\Regions{9-2}}%  010
              {\unexpanded{\allowbreak\cup \overline{A}\cap B \cap\overline{C}}}%
              {}%
           \xintifboolexpr{\Regions{9-3}}% 011
              {\unexpanded{\allowbreak\cup \overline{A} \cap B \cap C}}%
              {}%
           \xintifboolexpr{\Regions{9-4}}% 100
              {\unexpanded{\allowbreak\cup A\cap \overline{B}\cap \overline{C}}}%
              {}%
           \xintifboolexpr{\Regions{9-5}}% 101
              {\unexpanded{\allowbreak\cup A\cap \overline{B}\cap C}}%
              {}%
           \xintifboolexpr{\Regions{9-6}}% 110
              {\unexpanded{\allowbreak\cup A\cap B\cap \overline{C}}}%
              {}%
           \xintifboolexpr{\Regions{9-7}}% 111
              {\unexpanded{\allowbreak\cup A\cap B \cap C}}%
              {}%
    }%
   \xintifForFirst{\def\x{\emptyset}}
                  {\oodef\x{\expandafter\gobbletwo\x}}%
   \begin{pspicture}(0,-2)(5,4)
   % I will leave here each Region as individual call, so a color can
   % be added by modifying this code
    \xintifboolexpr{\Regions{9-0}}{\arealI[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-1}}{\arealII[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-2}}{\arealIII[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-3}}{\arealIV[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-4}}{\arealV[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-5}}{\arealVI[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-6}}{\arealVII[cyan][0.8]}{}%
    \xintifboolexpr{\Regions{9-7}}{\arealVIII[cyan][0.8]}{}%
    \EndeEllipsen{\parbox{4cm}{\centering$\x$}}%
   \end{pspicture}%
}%

缺陷：集合的描述是原子事件的不相交并集。可能有一些规范的较短描述，但我从未真正考虑过。例如，其中一个图表将表示 $\Omega\setminus A$，但这不是它被图例化的方式。

这个例子的实现方式如下（在文档的第 16 页，没有其他内容，即它对应于循环中的 #1 = 15，15=1111 表示保留原子事件 0=000、1=001、2=010、3=011，它是 Omega 中 A 的补码。

---

---

现在4 组。

这次，使用 TikZ 代码（我既不懂 PSTricks 也不懂 TikZ，只能通过复制预先存在的绘图说明来生存；在这种情况下，我从https://tex.stackexchange.com/a/100091/4686由@JohnHammersley 于 2013 年创作。

首先，我包含所有原子事件的图像，这些事件是代码中的宏接下来引用的区域\Atomic...。（这是为了在准备答案时进行检查）

这是 的代码 \VennFromTeX，将其用作\VennFromTeX{$ set formula with A, B, C, D $}。与上面针对三个集合的说明相同。（人们可能希望扩大语法，例如，允许使用U或\Omega并在 xintexpr 中将其定义为1，类似地\emptyset可以将其定义为0）。

\documentclass[12pt, tikz, border=10pt]{standalone}

\usepackage{tikz} 

\usetikzlibrary{positioning,shapes.geometric}

\usepackage{xintexpr}% for \VennFromTeX


% For drawing
\def\firstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
\def\secondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
\def\thirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
\def\fourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

\def\bounding{(-5,-3) rectangle (5,4)}

% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
\def\Atomic{% 0000
        \begin{scope}[even odd rule]% exterior
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \bounding;
        \end{scope}
}%
\def\Atomici{% 0001
        \begin{scope}[even odd rule]% fourth ellipse corner
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
        \fill[yellow] \fourthellip;
        \end{scope}
}%
\def\Atomicii{% 0010
        \begin{scope}[even odd rule]% third ellipse corner
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \thirdellip;
        \end{scope}
}%
\def\Atomiciii{% 0011
        \begin{scope}[even odd rule]%
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \fourthellip;
        \fill[yellow] \thirdellip;
        \end{scope}
}%
\def\Atomiciv{% 0100
        \begin{scope}[even odd rule]% second ellipse corner
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \secondellip;
        \end{scope}
}%
\def\Atomicv{% 0101
        \begin{scope}[even odd rule]%
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip;
        \fill[yellow] \secondellip;
        \end{scope}
}%
\def\Atomicvi{% 0110
        \begin{scope}[even odd rule]%
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \thirdellip;
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \secondellip;
        \end{scope}
}%
\def\Atomicvii{% 0111
        \begin{scope}[even odd rule]%
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \thirdellip;
            \clip \fourthellip;
        \fill[yellow] \secondellip;
        \end{scope}
}%
\def\Atomicviii{% 1000
        \begin{scope}[even odd rule]%
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicix{% 1001
        \begin{scope}[even odd rule]%
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip;
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicx{% 1010
        \begin{scope}[even odd rule]%
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip;
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicxi{% 1011
        \begin{scope}[even odd rule]%
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip;
            \clip \fourthellip;
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicxii{% 1100
        \begin{scope}[even odd rule]%
            \clip \secondellip;
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicxiii{% 1101
        \begin{scope}[even odd rule]%
            \clip \secondellip;
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip;
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicxiv{% 1110
        \begin{scope}[even odd rule]%
            \clip \secondellip;
            \clip \thirdellip;
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \firstellip;
        \end{scope}
}%
\def\Atomicxv{% 1111
        \begin{scope}[even odd rule]%
            \clip \secondellip;
            \clip \thirdellip;
            \clip \fourthellip;
        \fill[yellow] \firstellip;
        \end{scope}
}%

\makeatletter
\newcommand\VennFromTeX[1]{\VennFromTeX@main #1}%

\def\VennFromTeX@main$#1${%
    \begingroup
        \xintglobaldefstrue
        \def\overline##1{!(##1)}% or not(##1)
        \def\cap{&&}% or 'and'
        \def\cup{||}% or 'or'
        \def\oplus{ 'xor' }%
        \def\setminus##1{\ifx(##1&&!(\else &&!(##1)\fi}%
        \let\bigl\empty
        \let\bigr\empty
        % ....
        % (add above all needed extra definitions: \let\Bigl\empty etc...) 
    \xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
    \endgroup
    \begin{tikzpicture}

    \xintFor* ##1 in {01}:
    {%
      \xintFor* ##2 in {01}:
      {%
        \xintFor* ##3 in {01}:
        {%
          \xintFor* ##4 in {01}:
          {%
             \xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
             {\csname
               Atomic\romannumeral\numexpr##1*8+##2*4+##3*2+##4\endcsname}%
             {}%
           }%
         }%
       }%
    }%
    \draw \bounding;

    % \fill[white] \firstellip;
    % \fill[white] \secondellip;
    % \fill[white] \thirdellip;
    % \fill[white] \fourthellip;

    \draw \firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
    \draw \secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
    \draw \thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
    \draw \fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

    \draw \bounding node [label=below left:$U$] {};

    \draw (0, 0) node [yshift=+4.4cm] {$#1$};

    \end{tikzpicture}
}%
\makeatother
\begin{document}

% \xintverbosetrue

\VennFromTeX{$A\cap B\cap C\cap D$}

\VennFromTeX{$(A\cap B)\cup (C\cap D)$}

\VennFromTeX{$(\overline{A}\cup\overline{B})\cap(\overline{C}\cup\overline{D})$}

% attention to use parentheses for disambiguating \setminus 

\VennFromTeX{$(A\cup B \cup C) \setminus(B\cup C\cup D)$}

\VennFromTeX{$(A\cup B \cup C) \cap (B\cup C\cup D)$}

\VennFromTeX{$((A\setminus (B\cup C\cup D)) \cup B\cap C\cap
  D)\setminus (A\cap B\cap C\cap D)$}

\end{document}

\setminus请仔细阅读有关输入中使用的警告。

最后

Answer 3

\documentclass[pstricks]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
  \pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{% 
    \pscircle(1.5;90){3}
    \pscircle(1.5;-30){3} 
    \pscircle(1.5;210){3} 
} 
\end{pspicture} 
\end{document}

其他一些简单的例子：

\documentclass[pstricks]{standalone}
\usepackage{pstricks}
\begin{document}
\begin{pspicture}(-3.2,-3.2)(3.2,3.2)
  \pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
  \psclip{\pscircle(-1,0.5){1.5}% these object(s) will clip
          \pscircle(1,0.5){1.5}}
    \pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
  \endpsclip
  \pscircle(-1,0.5){1.5}% to get the clipped circle lines
  \pscircle(0,-1){1.5}
  \pscircle(1,0.5){1.5}
\end{pspicture}

\begin{pspicture}(-3.2,-3.2)(3.2,3.2)
  \pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
  \psclip{\pscircle(-1,0.5){1.5}}
    \pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
    \pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
  \endpsclip
  \pscircle(-1,0.5){1.5}
  \pscircle(0,-1){1.5}
  \pscircle(1,0.5){1.5}
\end{pspicture}

\begin{pspicture}(-3.2,-3.2)(3.2,3.2)
  \pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
  \psclip{\pscircle(0,-1){1.5}}
    \pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
    \pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
  \endpsclip
  \pscircle(-1,0.5){1.5}
  \pscircle(0,-1){1.5}
  \pscircle(1,0.5){1.5}
\end{pspicture}

\begin{pspicture}(-3.2,-3.2)(3.2,3.2)
  \pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
  \psclip{\pscircle(0,-1){1.5}}
    \pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
  \endpsclip
  \pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
  \pscircle(0,-1){1.5}
  \pscircle(1,0.5){1.5}
\end{pspicture}

\end{document}

Answer 4

按照此定义，每个表面都可以被着色。

\documentclass[pstricks]{standalone}
\usepackage{pst-node}
\usepackage{xparse,xintexpr}

\def\radiusK{\xinttheiexpr[6] 2*sqrt(3)/3\relax}

\def\KOEA{2.5,2}
\def\FOEA{\radiusK,\radiusK}

\def\KOEB{2,1}
\def\FOEB{\radiusK,\radiusK}

\def\KOEC{3,1}
\def\FOEC{\radiusK,\radiusK}

\def\KOEO{2.5,1.375}
\def\FOEO{2.5,2.5}

%uncomment the following lines to have ellipses
%\def\KOEA{1.9,2.2}
%\def\FOEA{1.4,1}
%
%\def\KOEB{3.3,2.2}
%\def\FOEB{1.2,1}
%
%\def\KOEC{2.75,1.4}
%\def\FOEC{1.4,1}
%
%\def\KOEO{2.5,2}
%\def\FOEO{2.5,2.0}

\NewDocumentCommand{\EreignisA}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEA)(\FOEA)}{%
\psellipse(\KOEA)(\FOEA)}%
}

\NewDocumentCommand{\EreignisB}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEB)(\FOEB)}{%
\psellipse(\KOEB)(\FOEB)}%
}

\NewDocumentCommand{\EreignisC}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEC)(\FOEC)}{%
\psellipse(\KOEC)(\FOEC)}%
}

\NewDocumentCommand{\EreignisOmega}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEO)(\FOEO)}{%
\psellipse(\KOEO)(\FOEO)}%
}

\NewDocumentCommand{\EndeEllipsen}{sm}{%
\EreignisOmega%
\pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
\pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
\EreignisA
\EreignisB
\EreignisC
\rput[t](E){#2}%
\IfBooleanF{#1}{%
\rput(Omega){$\Omega$}\pcline[nodesepA=0.25](Omega)(MOmega)
\rput(A){$A$}\pcline[nodesepA=0.25](A)(MA)
\rput(B){$B$}\pcline[nodesepA=0.25](B)(MB)
\rput(C){$C$}\pcline[nodesepA=0.2](C)(MC)
}%
}

\NewDocumentCommand{\codeclip}{m}{%
\pscustom[linestyle=none]{%
 \code{/clip /eoclip load def}%
  \psframe(-\maxdimen,-\maxdimen)(\maxdimen,\maxdimen)
  #1
  }%
}

\NewDocumentCommand{\arealI}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisOmega*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisB*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVI}{O{cyan}!O{0.8}}{%
\psclip{\EreignisB}
        \psclip{\EreignisC}%
                \EreignisA*[#1][#2]%
        \endpsclip
\endpsclip
}

\NewDocumentCommand{\arealVII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisA
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}

\begin{document}


\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\EndeEllipsen*{$A\setminus C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealVI
\EndeEllipsen*{$A\cap B\cap C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealIII
\arealV
\arealVI
\EndeEllipsen*{$A\cap (B\cup C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\EreignisC*%
\EndeEllipsen*{$(\overline{A}\cap \overline{B})\cup C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\arealIV
\arealVIII
\EndeEllipsen*{$\overline{A}\setminus (B\cap C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealVIII
\EndeEllipsen*{$(\overline{A}\setminus B)\cap C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealII
\arealV
\arealVI
\arealVII
\EndeEllipsen*{$(A\setminus B)\cup (B\cap C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealIII
\arealV
\EndeEllipsen*{$\bigl((A\cap B)\cup (A\cap C)\bigr)\setminus(A\cap B\cap C)$}
\end{pspicture}


\end{document} 

也许您想检查一下这个。

\documentclass[pstricks]{standalone}
\usepackage{pst-node}
\usepackage{xparse,xintexpr}

%\def\radiusK{\xinttheiexpr[6] 2*sqrt(3)/3\relax}
%
%\def\KOEA{2.5,2}
%\def\FOEA{\radiusK,\radiusK}
%
%\def\KOEB{2,1}
%\def\FOEB{\radiusK,\radiusK}
%
%\def\KOEC{3,1}
%\def\FOEC{\radiusK,\radiusK}
%
%\def\KOEO{2.5,1.375}
%\def\FOEO{2.5,2.5}

%uncomment the following lines to have ellipses
\def\KOEA{1.9,2.2}
\def\FOEA{1.4,1}

\def\KOEB{3.3,2.2}
\def\FOEB{1.2,1}

\def\KOEC{2.75,1.4}
\def\FOEC{1.4,1}

\def\KOEO{2.5,2}
\def\FOEO{2.5,2.0}

\NewDocumentCommand{\EreignisA}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEA)(\FOEA)}{%
\psellipse(\KOEA)(\FOEA)}%
}

\NewDocumentCommand{\EreignisB}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEB)(\FOEB)}{%
\psellipse(\KOEB)(\FOEB)}%
}

\NewDocumentCommand{\EreignisC}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEC)(\FOEC)}{%
\psellipse(\KOEC)(\FOEC)}%
}

\NewDocumentCommand{\EreignisOmega}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEO)(\FOEO)}{%
\psellipse(\KOEO)(\FOEO)}%
}

\NewDocumentCommand{\EndeEllipsen}{sm}{%
\EreignisOmega%
\pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
\pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
\EreignisA
\EreignisB
\EreignisC
\rput[t](E){#2}%
\IfBooleanF{#1}{%
\rput(Omega){$\Omega$}\pcline[nodesepA=0.25](Omega)(MOmega)
\rput(A){$A$}\pcline[nodesepA=0.25](A)(MA)
\rput(B){$B$}\pcline[nodesepA=0.25](B)(MB)
\rput(C){$C$}\pcline[nodesepA=0.2](C)(MC)
}%
}

\NewDocumentCommand{\codeclip}{m}{%
\pscustom[linestyle=none]{%
 \code{/clip /eoclip load def}%
  \psframe(-\maxdimen,-\maxdimen)(\maxdimen,\maxdimen)
  #1
  }%
}

\NewDocumentCommand{\arealI}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisOmega*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisB*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVI}{O{cyan}!O{0.8}}{%
\psclip{\EreignisB}
        \psclip{\EreignisC}%
                \EreignisA*[#1][#2]%
        \endpsclip
\endpsclip
}

\NewDocumentCommand{\arealVII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisA
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}

\begin{document}


\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\EndeEllipsen{$A\setminus C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealVI
\EndeEllipsen{$A\cap B\cap C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealIII
\arealV
\arealVI
\EndeEllipsen{$A\cap (B\cup C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\EreignisC*%
\EndeEllipsen{$(\overline{A}\cap \overline{B})\cup C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealI
\arealIV
\arealVIII
\EndeEllipsen{$\overline{A}\setminus (B\cap C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealVIII
\EndeEllipsen{$(\overline{A}\setminus B)\cap C$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealII
\arealV
\arealVI
\arealVII
\EndeEllipsen{$(A\setminus B)\cup (B\cap C)$}
\end{pspicture}

\begin{pspicture}[shift=-4](0,-1)(5,4)
\arealIII
\arealV
\EndeEllipsen{$\bigl((A\cap B)\cup (A\cap C)\bigr)\setminus(A\cap B\cap C)$}
\end{pspicture}


\end{document} 

在 xint-package 的帮助下，使用 xintFor 和 xintForpair，你可以编写

\VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%

所以每个表面都会有自己的颜色，或者你写

\VennIII[blue](0.5){2,4,6,8}{Text}%

并且全部变为蓝色，不透明度为 0.5。

\documentclass[pstricks]{standalone}
\usepackage{pst-node}
\usepackage{xparse,xintexpr}

\def\KOEA{1.9,2.2}
\def\FOEA{1.4,1}

\def\KOEB{3.3,2.2}
\def\FOEB{1.2,1}

\def\KOEC{2.75,1.4}
\def\FOEC{1.4,1}

\def\KOEO{2.5,2}
\def\FOEO{2.5,2.0}

\NewDocumentCommand{\EreignisA}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEA)(\FOEA)}{%
\psellipse(\KOEA)(\FOEA)}%
}

\NewDocumentCommand{\EreignisB}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEB)(\FOEB)}{%
\psellipse(\KOEB)(\FOEB)}%
}

\NewDocumentCommand{\EreignisC}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEC)(\FOEC)}{%
\psellipse(\KOEC)(\FOEC)}%
}

\NewDocumentCommand{\EreignisOmega}{sO{cyan}!O{0.8}}{%
\IfBooleanTF{#1}{%
\psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](\KOEO)(\FOEO)}{%
\psellipse(\KOEO)(\FOEO)}%
}

\NewDocumentCommand{\EndeEllipsen}{sm}{%
\EreignisOmega%
\pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
\pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
\EreignisA
\EreignisB
\EreignisC
\rput[t](E){#2}%
\IfBooleanF{#1}{%
\rput(Omega){$\Omega$}\pcline[nodesepA=0.25](Omega)(MOmega)
\rput(A){$A$}\pcline[nodesepA=0.25](A)(MA)
\rput(B){$B$}\pcline[nodesepA=0.25](B)(MB)
\rput(C){$C$}\pcline[nodesepA=0.2](C)(MC)
}%
}

\NewDocumentCommand{\codeclip}{m}{%
\pscustom[linestyle=none]{%
 \code{/clip /eoclip load def}%
  \psframe(-\maxdimen,-\maxdimen)(\maxdimen,\maxdimen)
  #1
  }%
}

%\ExplSyntaxOn
\NewDocumentCommand{\arealI}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
}%
\codeclip{%
  \EreignisB
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisOmega*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIII}{!O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealIV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisC
}%
\codeclip{%
  \EreignisC
}%
}%
\EreignisB*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealV}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisA*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVI}{O{cyan}!O{0.8}}{%
\psclip{\EreignisB}%
        \psclip{\EreignisC}%
                \EreignisA*[#1][#2]%
        \endpsclip
\endpsclip
}

\NewDocumentCommand{\arealVII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
  \EreignisC
}%
\codeclip{%
  \EreignisA
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}

\NewDocumentCommand{\arealVIII}{O{cyan}!O{0.8}}{%
\psclip{%
\codeclip{%
  \EreignisA
  \EreignisB
}%
\codeclip{%
  \EreignisB
}%
}%
\EreignisC*[#1][#2]%
\endpsclip
}
%\ExplSyntaxOff

\NewDocumentCommand{\VIIIarea}{O{cyan}O{0.8}m}{%
\xintifboolexpr{#3=1}{\arealI[#1][#2]}{}%
\xintifboolexpr{#3=2}{\arealII[#1][#2]}{}%
\xintifboolexpr{#3=3}{\arealIII[#1][#2]}{}%
\xintifboolexpr{#3=4}{\arealIV[#1][#2]}{}%
\xintifboolexpr{#3=5}{\arealV[#1][#2]}{}%
\xintifboolexpr{#3=6}{\arealVI[#1][#2]}{}%
\xintifboolexpr{#3=7}{\arealVII[#1][#2]}{}%
\xintifboolexpr{#3=8}{\arealVIII[#1][#2]}{}%
}

\NewDocumentCommand{\VennIII}{oD(){0.8}m!g}{%
\IfValueTF{#1}%
    {%
        \xintFor ##1 in {#3}\do {\VIIIarea[#1][#2]{##1}}%
    }%
    {%
        \xintForpair ##1##2 in {#3}\do {\VIIIarea[##2][#2]{##1}}%
    }%
\EndeEllipsen{\IfValueT{#4}{#4}}%
}

\begin{document}

\begin{pspicture}(0,-1)(5,4)
\VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[orange]{6}{$A\cap B\cap C$}%
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[cyan]{3,5,6}{$A\cap (B\cup C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[magenta](0.5){1,5,6,7}{$(\overline{A}\cap \overline{B})\cup C$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[green](0.2){1,4,8}{$\overline{A}\setminus (B\cap C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[cyan]{8}{$(\overline{A}\setminus B)\cap C$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(A\setminus B)\cup (B\cap C)$}
\end{pspicture}

\begin{pspicture}(0,-1)(5,4)
\VennIII[cyan]{3,5}{$\bigl((A\cap B)\cup (A\cap C)\bigr)\setminus(A\cap B\cap C)$}
\end{pspicture}


\end{document}